Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
440 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21425768 | C2 | semidirect |
| 2. #21425746 | C2 | semidirect |
| 3. #21424644 | C2 | semidirect |
| 4. #21424624 | C2 | semidirect |
| 5. #21424381 | C2 | semidirect |
| 6. #21422225 | C2 | semidirect |
| 230. C59 | #13432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425768 | 2 |
| #21425746 | 2 |
| #21424644 | 2 |
| #21424624 | 2 |
| #21424381 | 2 |
| #21422225 | 2 |
| C59×#3199 | 2 |
| #13432 | 59 |